In how many ways can the letters of the word ‘ASSASSINATION’

Question:

In how many ways can the letters of the word ‘ASSASSINATION’ be arranged so that all S’s are together?

Solution:

To find: number of ways letters can be arranged such that all S’s are together

Let all S’s be represented by a single letter Z

New word is AAINATIONZ

Number of arrangements $=\frac{10 !}{3 ! 2 ! 2 !}=151200$

Letters can be arranged in 151200 ways

 

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